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A073384 Seventh convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. 1
1, 16, 152, 1104, 6756, 36624, 181224, 834768, 3628746, 15035504, 59829704, 229977904, 857894388, 3117321456, 11067753144, 38492230704, 131417200419, 441252045408, 1459330704656, 4760342849504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n) = sum(b(k) * c(n-k), k=0..n) with b(k) := A000129(k+1) and c(k) := A073383(k).

a(n) = sum((2^n) * binomial(n-k+7, 7) * binomial(n-k, k) * (1/4)^k, k=0..floor(n/2)).

a(n) = ((34083315+46659654*n+24858030*n^2+6632968*n^3+939632*n^4+67304*n^5+ 1912*n^6)*(n+1)*U(n+1)+(7204365+13225068*n+8230910*n^2+2411744*n^3+ 362968*n^4+27088*n^5+792*n^6)*(n+2)*U(n))/(2^18*3^2*5*7), with U(n) := A000129(n+1), n>=0.

G.f.: 1/(1-(2+x)*x)^8.

a(n) = F'''''''(n+8, 2)/7!, that is, 1/7! times the 7th derivative of the (n+8)th Fibonacci polynomial evaluated at x=2. - T. D. Noe, Jan 19 2006

CROSSREFS

Eighth (m=7) column of triangle A054456, A073383.

Sequence in context: A240424 A225915 A023014 * A022644 A297090 A279323

Adjacent sequences:  A073381 A073382 A073383 * A073385 A073386 A073387

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified August 25 21:00 EDT 2019. Contains 326324 sequences. (Running on oeis4.)